Advertisements
Advertisements
प्रश्न
(x + 2)3
Advertisements
उत्तर
\[\frac{d}{dx}\left( f(x) \right) = \lim_{h \to 0} \frac{f\left( x + h \right) - f\left( x \right)}{h}\]
\[ = \lim_{h \to 0} \frac{\left( x + h + 2 \right)^3 - \left( x + 2 \right)^3}{h}\]
\[ = \lim_{h \to 0} \frac{\left( x + h + 2 - x - 2 \right)\left[ \left( x + h + 2 \right)^2 + \left( x + h + 2 \right)\left( x + 2 \right) + \left( x + 2 \right)^2 \right]}{h}\]
\[ = \lim_{h \to 0} \frac{h\left[ \left( x + h + 2 \right)^2 + \left( x + h + 2 \right)\left( x + 2 \right) + \left( x + 2 \right)^2 \right]}{h}\]
\[ = \lim_{h \to 0} \left[ \left( x + h + 2 \right)^2 + \left( x + h + 2 \right)\left( x + 2 \right) + \left( x + 2 \right)^2 \right]\]
\[ = \left[ \left( x + 0 + 2 \right)^2 + \left( x + 0 + 2 \right)\left( x + 2 \right) + \left( x + 2 \right)^2 \right]\]
\[ = \left( x + 2 \right)^2 + \left( x + 2 \right)^2 + \left( x + 2 \right)^2 \]
\[ = 3 \left( x + 2 \right)^2\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of x2 – 2 at x = 10.
Find the derivative of x at x = 1.
Find the derivative of x–4 (3 – 4x–5).
Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
(x + a)
Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
`(px^2 +qx + r)/(ax +b)`
Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
(ax + b)n
Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
`(a + bsin x)/(c + dcosx)`
Find the derivative of f (x) = x2 − 2 at x = 10
Find the derivative of f (x) = tan x at x = 0
Find the derivative of the following function at the indicated point:
sin 2x at x =\[\frac{\pi}{2}\]
\[\frac{1}{\sqrt{x}}\]
\[\frac{x + 1}{x + 2}\]
x ex
Differentiate each of the following from first principle:
\[\sqrt{\sin 2x}\]
Differentiate each of the following from first principle:
\[e^{x^2 + 1}\]
Differentiate each of the following from first principle:
\[e^\sqrt{ax + b}\]
Differentiate each of the following from first principle:
\[3^{x^2}\]
tan2 x
\[\frac{( x^3 + 1)(x - 2)}{x^2}\]
\[If y = \sqrt{\frac{x}{a}} + \sqrt{\frac{a}{x}}, \text{ prove that } 2xy\frac{dy}{dx} = \left( \frac{x}{a} - \frac{a}{x} \right)\]
Find the rate at which the function f (x) = x4 − 2x3 + 3x2 + x + 5 changes with respect to x.
xn loga x
sin x cos x
x2 sin x log x
(1 +x2) cos x
x3 ex cos x
x−3 (5 + 3x)
Differentiate in two ways, using product rule and otherwise, the function (1 + 2 tan x) (5 + 4 cos x). Verify that the answers are the same.
\[\frac{1 + \log x}{1 - \log x}\]
\[\frac{4x + 5 \sin x}{3x + 7 \cos x}\]
\[\frac{x^5 - \cos x}{\sin x}\]
\[\frac{x}{\sin^n x}\]
Write the value of the derivative of f (x) = |x − 1| + |x − 3| at x = 2.
If f (x) = |x| + |x−1|, write the value of \[\frac{d}{dx}\left( f (x) \right)\]
Mark the correct alternative in of the following:
If \[y = \sqrt{x} + \frac{1}{\sqrt{x}}\] then \[\frac{dy}{dx}\] at x = 1 is
Mark the correct alternative in each of the following:
If\[y = \frac{\sin x + \cos x}{\sin x - \cos x}\] then \[\frac{dy}{dx}\]at x = 0 is
Mark the correct alternative in of the following:
If \[y = \frac{\sin\left( x + 9 \right)}{\cos x}\] then \[\frac{dy}{dx}\] at x = 0 is
Find the derivative of f(x) = tan(ax + b), by first principle.
